A. Yu. Smirnov A. Yu. Smirnov
before nu2012 G. L. Fogli Serious implications for theory Non-zero, relatively Large 1-3 mixing Substantial deviation of the 2-3 mixing from maximal d CP ~ p DB new Robust ?
d 23 = ½ - sin 2 q 23 n m - n t symmetry violation the key to ( probe) Connection to understand the 1-3 mixing underlying physics Quark -Lepton q 23 ~ p /2 - V cb Complementarity Fogli et al, 1 s MINOS, 1 s SK, 90% NH sin 2 q 23 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70
sub-GeV F e n e - oscillation F e0 - 1 = P e2 (r c 232 - 1) range effects = P e3 (rs 232 – r) multi-GeV range r = F m 0 /F e0 ~ 2 ``screening factor’’ The e-like event excess – ar low energies and deficit at higher energies - signature of deviation of the 2-3 mixing from maximal (first quatrant) P m e ~ sin 2 q 13 sin 2 q 23 - appearance P mm ~ sin 2 2 q 23 - disappearance
Third way Neutrino- antineutrino asymmery Key measurement: amplitudes of the n m - n m oscillations due to solar and atmospheric mass splittings Do we have predictions for the phase in quark sector? G. L. Fogli Why do we think that we can predict leptonic mixing? Again because of neutrinos are special ? Symmetries? First glimpses? T . Yanagida d CP ~ p /2 +/- 0.02
sin 2 q 13 ~ 0.025 The same 1-3 mixing with completely different implications D m 212 ``Naturalness’’ of mass matrix O(1) D m 322 ~ ½ sin 2 q C Quark Lepton Complementarity sin 2 q 13 = n m - n t - symmetry violation ~ ½cos 2 2 q 23 A. De Gouvea, Mixing anarchy > 0.025 H .Murayama Self-complementarity q 13 + q 12 = q 23 ~ p/4
With different implications
Mixing appears as a result of different ways of the flavor symmetry breaking in neutrino and charged lepton sectors G f A 4 T 7 S 4 Residual G l G n T’ symmetries ? M n M l 1 n TBM-type diagonal the splitting originates from different flavor assignments of the RH components of N c and l c and different higgs multiplets
If G is von Dyck group D(2, m, p) D. Hernandez, A.S. For column of the mixing matrix: A 4 |U b i | 2 = |U g i | 2 S 4 1 – a |U a i | 2 = 4 sin 2 ( p k/m) A is determined from condition d = 77 0 l 3 + a l 2 - a* l - 1 = 0 l ip = 1 S 4 k, m, p integers which Also S. F. Ge, D. A. Dicus, determine symmetry group W. W. Repko, PRL 108 (2012) 041801
q 13 ~ ½ q c First obtained in the context of sin 2 q 13 ~ ½sin 2 q C Quark-Lepton Complementarity H. Minakata, A Y S Follows from U 12 ( q c ) U 23 ( p /2) permutation of matrices From charged Maximal from leptons neutrinos Permutation - to reduce the lepton mixing matrix to the standard form Related to smallness of mass
sin 2 q 13 ~ sin 2 q 23 sin 2 q C D. Hernandez, A.S. Improves also predictions for 1-2 mixing Bi-maximal mixing? RGE effect sin 2 q 13 ~ sin 2 q 23 sin 2 q C
P. Ramond Deviations from BM due to high order corrections Complementarity: Weak complementarity or Altarelli et al implies quark-lepton Cabibbo haze symmetry or GUT, Corrections from high order or horizontal symmetry flavon interactions generate Cabibbo mixing and deviation from BM, GUT is not necessary m m sin q C = 0.22 sin q C = as ``quantum’’ of m t flavor physics Self-complementarity relations Xinyi Zhang Bo-Qian Ma, arXiv:1202.4258
Similar Ansatz for M Fukugita T. Yanagida structure of mass matrices Relations between Fritsch Anzatz similar to quark sector masses and mixing 3 RH neutrinos with equal masses Normal mass hierarhy, Right value of 13 mixing Flavor ordering
Values of elements gradually decrease from m tt to m ee corrections wash out sharp difference of elements of the dominant mt -block and the subdominant e-line This can originate from power dependence of elements on large expansion parameter l ~ 0.7 – 0.8 . Another complementarity: l = 1 - q C Froggatt-Nielsen?
D m 21 2 sin 2 q 13 ~ D m 32 2 1. Two mass scales in the mass matrix D m 312 D m 212 2. Two large mixing angles 3. Normal mass hierarchy 4. No fine tuning - no equalities of matrix elements sin q 13 ~ D m 212 / D m 312 = 0.17 - 0.20 - no particular (for leptons) flavor symmetries, - normal mass hierarchy
After many speculations back to good old picture? Something is High scale seesaw still missed The same mechanism which explains smallness of neutrino mass is responsible for large lepton mixing Difference of quark and lepton mixings is related to smallness of neutrino mass
RH-neutrino u r , u b , u y , n u rc , u bc , u yc , n c d r , d b , d y , e d rc , d bc , d yc , e c S S S S S S - Enhance mixing S S S S - Produce randomness (anarchy) S S S - Seesaw symmetries S S S - Increase seesaw scale S S S - produce bi-maximal mixing S S S S S S S S S S Hidden sector B. Feldstein, W. Klemm Statistical distribution … arXiv: 1111.6690
M. Smy No distortion of the energy spectrum Increasing tension between D m 221 at low energies : the upturn is disfavored measured by KamLAND and in at (1.1 – 1.9) s level solar neutrinos 1.3 s level This is how new physics may show up
pp 7 Be CNO 8 B pep . SNO n e - survival probability from solar neutrino data vs LMA-MSW solution HOMESTAKE SNO+ low rate
n e n s n t n m Very light sterile neutrino n 3 m 0 ~ 0.003 eV DE scale? M 2 M ~ 2 - 3 TeV M Planck D m 231 mass n 2 - solar neutrino data D m 221 n 0 D m 2dip n 1 sin 2 2 a ~ 10 -3 sin 2 2 b ~ 10 -1
P. de Holanda, AYS m 0 ~ 0.003 eV M 2 m 0 = M Planck M ~ 2 - 3 TeV
Accumulating data at SK SK I - IV Day-Night effect: at 2.3 s – level in agreement with the LMA MSW solution New precision level - new possibilities: HyperKamiokande, LENA, MICA
Be neutrino line A Ioanissian, AYS Period of width of oscillations Beryllium ~ in energy nu line scale Width of the Be nu line central temperature of the Sun Precise measurements of D m 212 Tomography of the Earth with resolution 20 km
Huge Atmospheric Neutrinos Detectors
Earth matter effect NOvA Energy spectrs Sterile neutrinos NH IH Neutrino beam may help? nu antinu Fermilab-PINGU(W. Winter)
Oscillation physics with Huge atmospheric neutrino detectors P. Coyle Oscillations 2.7 s ANTARES G. Sullivan Oscillations at high energies 10 – DeepCore 100 GeV in agreement with low energy data Ice Cube no oscillation effect at E > 100 GeV Bounds on non-standard interaction, Lorentz violation etc
Precision IceCube Next Generation Upgrade PINGU v2 Denser array 20 new strings (~60 DOMs each) in 30 MTon DeepCore volume Few GeV threshold in inner 10 Mton volume Energy resolution ~ 3 GeV Existing IceCube strings Existing DeepCore strings New PINGU-I strings 125 m
High statistics can cure other problems
E. Akhmedov, S. Razzaque, A. Y. Smirnov 2 GeV, 11.25 0 arXiv: 1205.7071 Smearing with Gaussian reconstruction functions characterized by (half) widths ( s E , s q ) 3 GeV,15 0 4 GeV, 22.5 0
s E = 0.2E s q ~ 1/E 0.5 Degeneracy
n e n s n t n m LSND/MiniBooNE: vacuum oscillations n 4 P ~ 4|U e4 | 2 |U m 4 | 2 restricted by short baseline exp. BUGEY, CHOOZ, CDHS, NOMAD mass D m 241 For reactor and source experiments n 3 D m 231 P ~ 4|U e4 | 2 (1 - |U e4 | 2 ) n 2 D m 221 n 1 With new reactor data: ( 0.89 eV 2 ) D m 412 = 1.78 eV 2 - additional radiation in the universe U m 4 = 0.23 - bound from LSS? U e4 = 0.15
In general For different mixing schemes Varying |U t 0 | 2 < 3% stat. error Zenith angle distribution depends on admixture of n t in 4 th mass state
sin 2 2 a = 10 -3 (red), 5 10 -3 (blue) SK-I SNO-LETA P. De Holanda, A.S. SK-III Borexino SNO-LETA R D = 0.2 D m 2 = 1.5 10 -5 eV 2
De Gouvea, Murayama
from global fits with salient probably features smallness of mass related Peculiar (?) pattern of mixing strongly differs from quark mixing - Mass hierarchy (ordering) - Deviation of 2-3 mixing from maximal - CP violation - Majorana nature - Absolute scale Sterile neutrinos Usual ``hard’’ masses Generated at the electroweak Not a small perturbation and higher mass scales of the standard framework
L. Wolfenstein P. F. Harrison D. H. Perkins W. G. Scott - maximal 2-3 mixing 2/3 1/3 0 - zero 1-3 mixing, no CP-violation - 1/6 1/3 - 1/2 U tbm = 0.6 - 1/6 1/3 1/2 - sin 2 q 12 = 1/3 0.8 n 3 is bi-maximally mixed n 2 is tri-maximally mixed Should be broken Mass matrix in flavor basis: Mass relations m e m = m e t a b b … c d m mm = m tt m TBM = … … c m ee + m e m = m mm + m mt
NH Strong suppression of Level crossing n e n 3 the neutronization peak: in the H-resonance is highly adiabatic Permutations of flavor spectra which depend on mass hierarchy Earth matter effects Shock wave effect Adiabaticity is broken in shock front if the relative width of the front: D R/R < 10 -4 10 km If the earth matter effect is if larger – no shock wave effect: observed for antineutrinos probe of the width of front NH is established!
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